West Ham have now lost their last six matches without scoring a goal and there could be a long winter ahead on this evidence for Alan Pardew and his team. Pardew's team worked hard enough and never gave up but once they had gone behind to a first-half goal they never looked like snatching even a draw.
Former West Ham keeper David James made two important saves from Paul Konchesky and Nigel Reo-Coker when Portsmouth were only a goal ahead, but when Portsmouth got their second with eight minutes remaining there was only going to be one winner.
Portsmouth's win keeps them among the early season pace-setters although they were made to work hard for their latest success.
Pardew, growing more desperate by the day, brought Teddy Sheringham in against his old club for his first start of the season. Sheringham inevitably brought class and flare but there was little scope for him and West Ham chances were rare.
Portsmouth took the lead in the 24th minute with a soft goal when Glen Johnson, another man with strong West Ham connections, centred from the right and Nwankwo Kanu got above Anton Ferdinand to beat Roy Carroll with a header into the corner of the net. West Ham appealed unsuccessfully for a foul on Ferdinand.
Kanu twice missed easy chances to add to his tally and by half-time the Hammers were lucky not to have been further adrift.
But they improved after the break and after 54 minutes James dived to his left to push away a fierce left-foot shot from the always adventurous Konchesky . James was also out quickly to block Hayden Mullins as he raced towards the goal and in the 81st minute made another save on his line to keep out Reo-Coker.
Referee Graham Poll was a busy man, booking four players from either side while Sol Campbell might have been further punished for a clumsy first-half challenge.
Redknapp sent on Andrew Cole and Lomana Tresor LuaLua near the end to increase West Ham's discomfort and it paid off in the 82nd minute. LuaLua, Matt Taylor and Cole all combined on the edge of the area and when West Ham failed to clear, Cole scored with a right-foot shot.
Pardew meanwhile took off Sheringham, who got an ovation from the Pompey fans, and Bobby Zamora and replaced them with Marlon Harewood and Carlton Cole but it made little difference as Portsmouth held on comfortably enough.
James, otherwise so sound and competent, got away with a miss-kick but West Ham created few openings and looked a side short of confidence. Their only win of the season was on the opening day and they have collected only five points in total.
Former West Ham manager Redknapp was delighted with his team's performance and they made the most of a Club in turmoil.
Referee Poll showed yellow cards to Gary O'Neil , Campbell, Miguel Pedro Mendes and Johnson of Portsmouth while there were cautions also for West Ham quartet Reo-Coker, Matthew Etherington, Sheringham and Konchesky of West Ham.